Study of Magnetic Field E�ects in Drift Tubes

for the Barrel Muon Chambers of the CMS

Detector at the LHC

M. Aguilar-Ben��tez a, M. Arneodo b, M. Benettoni c,

A. Benvenuti d, J. Berdugo a, S. Bethke e, M. Cerrada a,

R. Cirio b, N. Colino a, F. Conti c, M. Dallavalle d, M. Daniel a,

F. Daudo b, M. De Giorgi c, A. De Min c, U. Dosselli c,

C. Fanin c, B. Fehr e, M.C. Fouz a, F. Gasparini c, U. Gasparini c,

R. Giantin c, V. Giordano d, P. Guaita c, M. Guerzoni d,

I. Lippi c, P. Ladr�on de Guevara a, S. Marcellini d, F. Mart��n a,

R. Martinelli c, S. Maselli b, A. Meneguzzo c, E. Migliori b,

J. Mochol�� a, A. Montanari d, F.L. Navarria d, F. Odorici d,

M. Pegoraro c, C. Peroni b, H. Reithler e, L. Romero a,

A. Romero b, P. Ronchese c, A.M. Rossi d, T. Rovelli d,

A.J. Sancho c, P. Sartori c, H. Schwartho� e, V. Sondermann e,

A. Staiano b, V. Tano e, H. Teykal e, E. Torassa c, J. Tutas e,

J. Vandenhirtz e, H. Wagner e, M. Wegner e, C. Willmott a,

P. Zotto c, G. Zumerle c

aCIEMAT - Divisi�on de F��sica de Part��culas, Madrid, Spain

bUniv. di Torino e Sez. dell' INFN, Torino, Italy

cUniv. di Padova e Sez. dell INFN, Padova, Italy

dUniv. di Bologna e Sez. dell' INFN, Bologna, Italy

eIII. Physikalisches Institut der RWTH Aachen, Germany

Abstract

The drift chambers in the barrel region of the CMS detector are exposed to magneticstray �elds. To study the performance of the muon reconstruction and the drifttime based muon trigger, prototypes were tested under the expected magnetic �eldconditions at the H2 test facility at CERN. The results indicate that the overallchamber performance will not be a�ected. Only the bunch crossing identi�cationcapability in the small region near � = 1:1, corresponding to the border of the solidangle region covered by the barrel, will be weakened.

Preprint submitted to Elsevier Preprint 27 March 1998

1 Introduction

The design goals of the barrel CMS drift chambers include muon identi�cation,track reconstruction and trigger capabilities [1]. The muon trigger is basedon a so called Mean Timing technique [2,3]. It requires a homogeneous driftvelocity as well as an adequate time resolution in order to resolve the protonbunch crossing frequency of 25 ns at the LHC. Results from prototypes with anoptimised drift cell design, in the absence of magnetic �eld, have been recentlypresented [4]. They show that the requirements for the muon reconstructionand triggering in the barrel muon system of CMS can be met. The selecteddrift gas, Ar:CO2(85:15) under normal conditions, is a compromise of low cost,low ageing propensity, and su�cient quenching ability with fast saturation.The drift cell design ensures a homogeneous electric �eld of approximately2 kV/cm except in the regions close to the anode and the cathode.

In CMS the barrel muon chambers will be exposed to magnetic stray �eldsvarying in orientation and magnitude along the chamber volume. Assuminga 4 T �eld inside the solenoid, stray �elds in the chambers are expected toremain well below 0.4 T with the exception of a small region where it can goup to 0.8 T. Under the in uence of crossed electric and magnetic �elds thelarge Lorentz angle of the gas will reduce the e�ective drift velocity. Providedthat the magnetic �eld is known in orientation and magnitude, corrections canbe applied during o�ine muon track reconstruction. At trigger level however,large variations of the magnetic �eld along the anode wires cannot be correctedfor.

In order to quantify the magnetic �eld e�ects on the Mean Timing procedure,and on the chamber performances, measurements were carried out with driftchamber prototypes at the H2 test beam area at CERN. The results obtainedare presented in this paper.

2 The Barrel Muon System

The central muon system of the CMS detector [1] consists of four muon sta-tions (MB1, MB2, MB3 and MB4) placed inside the iron return yoke of asuperconducting solenoidal magnet as shown in �g. 1. It is built up by �veconcentrical rings enclosing the coil and the inner detectors.

The central and adjacent rings are separated by 15 cm (space needed for thecabling of the subdetectors and the cryogenic support system). Separationdistances in between the outer rings are 12 cm.

2

In the transverse view the muon stations are divided in 12 sectors, thus eachcovering an angle range of 30�. In each muon station the bending of the muontrack in the transverse projection is measured in two groups of 4 layers of drifttubes (� layers). Another group of four layers (� layers), measure the projectionalong the proton beam axis. The groups of 4 layers are called quadruplets orsuperlayers. Adjacent layers in a quadruplet are staggered by half a cell.

The magnet has been designed [7] to provide a homogeneous magnetic �eldof 4 T parallel to the proton beam axis inside the coil volume. The iron ofthe yoke is saturated by the returning magnetic �eld lines with a magnitudeclose to 1.8 T. The inhomogeneous �eld lines at the end of the coil and in thegaps between the return yoke rings are leaking into the four muon stations. Inaverage the magnetic �eld has a good symmetry around the beam line axis.Their components perpendicular (Br) and parallel (Bz) to the proton beamaxis are shown in �g. 2.

The parallel component Bz stays approximately constant in each of the muonstations and is rarely larger than 0.2 T. It rises up to 0.3 or 0.4 T only inthe last centimeters of the chambers (this space is partly used for mechanicalsupport of the wires and for electrical connections).

The strongest variations in the radial magnetic �eld component Br are in theforward ring. There Br varies from 0.2 to 0.8 T along the station MB1. InMB2 it reaches a value close to 0.35 T but stays approximately constant. InMB4 the sign of the magnetic �eld component changes, although its absolutevalue does not get larger than 0.2 T. A similar behaviour holds for MB4 inthe middle ring. In all the other stations the magnetic �eld stays always below0.2 T.

2.1 Magnetic Field E�ects

In the case of crossed magnetic and electric �elds the drift of electrons isin uenced by the Lorentz force according to the expression

vdrift =e

me

� jEj1

1 + (!�)2(~E+ !� [ ~E� ~B] + (!�)2(~E ~B) ~B) (1)

with me, e� mass and charge of the electron, ! the cyclotron frequency, � the

electron collision frequency and ~E, ~B the normal �eld vectors (see e.g. [8]). If�elds are orthogonal, the drift velocity can be simply parametrized as

vdrift(E;B) = vdrift(E; 0) cos(�L(E;B)) (2)

3

with �L the Lorentz angle. The value of �L depends on the electric and mag-netic �eld strength and must be measured for any drift gas mixture.

In Ar:CO2(85:15) one measures for an electric �eld strength of 2 kV/cm aLorentz angle of 12� for B = 0.5 T and 18� for B = 0.83 T [6]. This wouldtranslate into an increase of the maximum drift time in the drift tubes ofapproximately 8 ns and 18 ns, respectively.

In the quadruplet local reference system, we call the three components of themagnetic �eld BN , BW and BE. The �rst one, BN , is orthogonal to the planede�ned by the wires in one layer, and also to the electric �eld. The other twocomponents, BW and BE, stay inside the wire plane: the former one is parallelto the wires and the latter one is parallel to the electric �eld.

In the simple picture of expression (1), neglecting anisotropic di�usion, BE

would not a�ect the drift velocity signi�cantly. Therefore, the main e�ectsshould come mainly from the components BW and BN . In particular BW

would distort the drift electron trajectories as shown in �g. 3, whereas BN

would introduce a longer drift path towards the anode, as sketched in �g. 4.

Naively one should expect that the only e�ect of BN is to change the e�ectivedrift velocity. In the case of BW , distortions of the drift lines may, in addition,produce ine�ciencies, because of decreasing the active cell volume, and mayalso a�ect the symmetry of the behaviour of the cell with respect to the angleof incidence.

We have measured the in uence of each of these three components of the B�eld using small size prototypes in a test beam at CERN during 1995 and 1996.From this study we can calculate the magnetic �eld e�ects to be expected ineach of the � and � layers of the �nal CMS barrel muon detector. In particular,� layers will be exposed to magnetic �eld components BN = Br cos �, BE =Br sin� and BW = Bz, whereas in the case of � layers BN = Br cos �, BE = Bz

and BW = Br sin�, � ranging approximately from -15� to 15�.

3 Experimental Setup

Several prototypes were installed inside the superconducting magnet M2 ofthe H2 test beam facility at CERN. Their main features were described in [4].All of them had in common the drift cell con�guration of �g. 3 and consistedof at least one quadruplet. Data were taken in two periods with di�erentorientations of the magnetic �eld with respect to the muon beam direction:

4

{ During 1995 the magnetic �eld was parallel to the incoming muon beam.This con�guration is ideal to study BN . Prototype chambers were placedorthogonal to the beam with anode wires in a vertical direction. A tilt ofthe chamber around a horizontal axis allowed to study combined BN andBW e�ects.

{ During 1996 the magnetic �eld was in a horizontal direction perpendicularto the beam. Superlayers with anode wires in a vertical direction were usedto measure BE e�ects, whereas superlayers with horizontal anode wiresprovided information on the in uence of BW .

Incoming muons had a momentum in the range 200 to 300 GeV/c. The setupallowed to rotate the chamber prototypes around an axis parallel or orthogonalto the anode wires in order to study the e�ects of di�erent angles of incidence.All prototypes were operating with the drift gas Ar:CO2(85:15) under normalconditions. As indicated in �g. 3, the voltages used were 3.6/1.8/-1.8 kV on an-ode/electrode/cathode (reference voltages in [4]). A signi�cant fraction of thedata was also taken with voltage settings at 3.3/1.5/-1.5 kV. The gain, con-trolled by the di�erence between the anode and electrode voltages, is similar inboth cases but the second setting provides a lower drift �eld as a consequenceof the smaller voltage di�erence between electrode and cathode.

4 Performance under BE and BW

4.1 Drift Velocity and Linearity

The so called \mean time" obtained from three consecutive layers, staggeredhalf a cell, according to

tMT =1

2(tj + tj+2) + tj+1 = tmaxdrift (3)

provides a measurement of the maximum drift time, and hence of the driftvelocity if a linear space-time relation is assumed. We present in �g. 5 theresults obtained for the drift velocity at several values of the magnetic �eld.As expected, �g. 5 shows no signi�cant change of the drift velocity as a functionof the magnetic �eld value BE. On the other hand, there is a clear e�ect in thecase of BW , the e�ective drift velocity decreasing as BW increases. The e�ectis small (of the order of 1 %) at BW = 0:4 T, and becomes very important athigh BW values ( greater than 5 % at BW = 1 T).

High BW �eld values are also expected to a�ect the linearity of the space-timerelation. Distortions should appear mainly in the region near the cathode I

5

beams. Evidence for these distortions can be found in the distributions ofthe residuals from a track �t assuming a constant drift velocity. The averagevalues of these �t residual distributions as a function of the distance to thewire calculated in 1 mm bin slices is shown in �g. 6 for two values of BW . Inthe case of BW = 0.8 T, linearity is quite good in the central region of the cell.However, it becomes much worse in the last few mm close to I beams wheredeviations from linearity become larger than 0.5 mm (because of the geometryof staggered adjacent layers, e�ects near the wire and near the I beams arestrongly correlated). On the other hand, as also shown in �g. 6, there are nosigni�cant deviations from linearity if BW stays below 0.2 T, which will bethe case in CMS.

4.2 Resolution

The width of the tMT variables provide an estimate of the single wire reso-lution. We show in �g. 7 the e�ect of the magnetic �eld on this resolutionvalue. Again, no dependence can be seen when B is parallel to the electric�eld. However, for B parallel to the wire, resolution gets clearly worse whenthe magnetic �eld increases. From �g. 7 one can see that for BW values smallerthan 0.4 T, the resolution is always better than 250 microns which is an ac-ceptable value. Since BW will never exceed 0.4 T in the active volume of thechambers at CMS, one can conclude that the e�ect of the component of themagnetic �eld along the wire on the resolution will not be a problem.

4.3 E�ciency

Tracks having 3 and 4 hits in the quadruplet are used to calculate the singlewire e�ciency. In �g. 8 a drop in e�ciency for high values of BW can beseen. Qualitatively this e�ect was expected from simulations. The distortionof the drift lines shown in �g. 3 becomes bigger as BW increases and it couldeventually produce a hole in the acceptance for muon tracks going throughthe �rst few millimeters away from the cathode I beams. This can be betterseen in �g. 9 which shows the e�ciency as a function of the distance to thewire for several values of BW . Below 0.4 T, the e�ciency is still high in thewhole drift volume.

On the other hand, as also shown in �g. 8, variations on BE do not a�ectchamber e�ciency in a signi�cant way.

6

4.4 Asymmetry e�ects

As indicated in �g. 3, the e�ect of BW on the drift lines can be seen as a rota-tion of the tube around its wire. This a�ects the symmetry of the behaviour ofthe cell with respect to tracks which have positive or negative angles comparedto normal incidence. The e�ect can be simulated by taking data at a givenangle of incidence with positive and negative magnetic �eld.

In �g. 10 the maximum drift time is shown as a function of BW for several an-gles of incidence. Asymmetry e�ects are clearly visible. One can see in �g. 10that even at B = 0 the maximum drift time is a�ected by the track angle ofincidence as previously observed [4]. From 0� to 24�, this variation amounts to7 ns. In the presence of a magnetic �eld of 0.1 T parallel to the wires, the varia-tion of the maximum drift time from -24� to 24� is increased to approximately12 ns. Most of the high pT muon tracks traversing the CMS barrel chamberswill stay inside this angular range. Bunch crossing identi�cation puts a con-straint on the acceptable maximum drift time variation. Basically it shouldnever exceed the interbunch time of 25 ns in order to avoid ine�ciencies ofthe trigger algorithm. Therefore asymmetry e�ects, although non negligible,are expected to have a minor in uence on the drift chamber trigger capabilityat CMS.

5 Performance under BN

5.1 Drift Velocity and Linearity

The simulated e�ect of a magnetic �eld component BN = 1 T on the electrondrift in the drift tubes is shown in �g. 11. Up to a drift distance of 2 mm theelectric �eld is very high. Therefore, the magnetic �eld de ection is small andthe drift velocity stays essentially unchanged.

For drift distances greater than 2 mm the drift velocity is constant to a goodapproximation. This re ects the small variations of the Lorentz angle at thegiven range of the electric �eld strength of (2.3�0.3) kV/cm for the nominalvoltages. In table 1 the average drift velocity, the corresponding maximumdrift time and the Lorentz angle are shown for two voltages and magnetic�eld settings.

Table 1 shows that with nominal high voltage settings the value of tMT in-creases by 27 ns when going from BN = 0 to BN = 1 T. This is certainly avery important e�ect which, if not corrected for, would spoil bunch crossing

7

identi�cation at the trigger level. In section 6 we will discuss the implicationsof this e�ect in the chamber performance at the expected working conditionsof the CMS experiment.

The mean time de�ned in (3) is expected to be independent of the incidentangle and the track position in the drift cell for a constant drift velocity. Thisis ful�lled to a good approximation in the magnetic �eld-less case, as shownfor example in �g. 12 for perpendicular tracks. This �gure also shows thatat BN = 1.0 T the presence of non linearities is quite clear (they could beof the order of 250 or 300 microns at most since the mean time value stayswithin a range of �5 ns the average of tMT ). Even if the e�ect of the reducede�ective drift velocity is properly taken into account, in the case of BN = 1 Tthe fraction of muon tracks which are within (tMT � 12:5)ns decreases by 5%when compared to the situation at BN =0 because of the non linearities.

5.2 Resolution

In �g. 13 the dependence of the single wire resolution with the magnetic �eldcomponent BN is shown. The plot includes several angles of incidence to takeaccount of the range covered by � layers in CMS. It shows that once the propere�ective drift velocity is taken into account there is no sizable degradation ofthe average spatial resolution. At BN = 1 T the resolution gets near to 280microns, which is still within the design goals for the drift tube chambers.

5.3 E�ciency

The single wire e�ciency, calculated in the drift volume, is shown in �g. 14.Also in this case the in uence of having di�erent angles of incidence wasstudied. At all BN values, even at 1 T, e�ciency is always bigger than 99%for the whole angular region measured.

6 Performance under BN and BW

The e�ect of combining the two magnetic �eld components, BN and BW , onthe mean timing performance is shown in �g. 15 for the case BN = 0.9 T andBW = 0.45 T. The comparison with �g. 12, and with the results presentedin section 4.1, show that BW is responsible for the strong degradation inthe linearity of the space-time relationship in the vicinity of the cathodes.Excluding these regions the resolution amounts to 235 �m.

8

7 Implications for operation at CMS

The most demanding restrictions on the resolution and timing properties applyto the drift tubes of the pT measuring �-layers in the barrel muon chambers.

The good homogeneity of the electric �eld and its high �eld strength makesthe drift tubes insensitive to values of BE up to 1 T.

As far as BN is concerned, the results demonstrate that both e�ciency andresolution measured up to 1 T stay well within the design goals. A more de-tailed discussion is necessary for the drift velocity and for absolute timingmeasurements. In each group of four layers inside the same quadruplet theMean Timing electronics identi�es the bunch crossing to which the particlebelongs with a �xed delay equal to the maximum drift time. To operate prop-erly the circuit must be tuned to the e�ective drift velocity. A time window isopened by the Bunch Crossing clock centered at the corresponding maximumdrift time and having a width large enough to account for the di�erent timeof ight and for the propagation time of the signals along the wire. There-fore, the increase in the maximum drift time produced by the presence of themagnetic �eld can be properly taken into account by increasing accordinglythe time delay of the window in steps of one nanosecond. This tuning wouldbe fully e�ective if the �eld is uniform along the wire length. A non uniform�eld however generates an additional dispersion on the maximum drift time.Corrections can of course be applied in the o�ine analysis in order to accountfor the magnetic �eld variation. Field uncertainties of 5% would introducemaximum errors comparable to the drift tube resolution at 1 T and negligi-ble errors below 0.5 T. Obviously this cannot be applied at the trigger level.Trigger capability is a�ected di�erently in di�erent chambers.

In MB2 to MB4 the normal component BN yields values which are less than0.4 T. The in uence of the increase of the maximal drift time at BN = 0.5 Tby 5 ns on the mean timing e�ciency is moderate, as can be estimated fromthe taken data even without a detailed simulation of the trigger electronicsimplementation. By simply taking a time window of 25 ns around the maxi-mum drift time at BN = 0 T, we �nd that the fraction of muon tracks in asingle triplet of drift cells at BN = 0.5 T which fall in that window decreasesby 8% with respect to the reference drift time. In an optimized time windowthe mean timing e�ciency decreases by 1% for muon tracks at 0 T and 5% at0.5 T.

In MB1 in the outer wheels however, BN rises from 0.2 to 0.8 T along theanode wires. Repeating the same exercise with the data taken at BN=0.5 Tand BN=1.0 T we �nd that if the time window is set for B=0.5 T values, themean timing e�ciency would decrease by 8% for muon tracks at B=0 and by

9

as much as 50% for muon tracks at B=1.0 T. This indicates that a degradationof the capability of an unambiguous Bunch Crossing identi�cation has to beexpected in the MB1 chambers near the barrel endcaps in the small regionclose to � = 1:1 (see �g. 1 and �g. 2). To try to reduce this e�ect by increasingthe electric �eld strength does not help much since the decrease in the Lorentzangle is marginal. Not much can be gained by changing the gas mixture either,because of the boundary conditions ensuring a fast saturated drift gas withlow ageing propensity. It should be anyhow stressed that the reported testresults apply to the expected performance of one independent superlayer. Theglobal trigger, being determined by at least two muon stations, will help insmoothing out the bad behaviour of crytical regions in single superlayers.

In the case of BW , the results show that its in uence becomes dramatic asthe magnetic �eld value increases. Not only the drift velocity changes verysigni�cantly above 0.5 T, but also resolution deteriorates signi�cantly ande�ciency losses are very important. It is fortunate that in CMS, BW will veryrarely exceed 0.2 T, and there the e�ects will have a minor in uence. Only theasymmetries a�ecting the behaviour of a layer with respect to its normal, asdescribed in section 4.4, should still be taken into consideration when de�ningthe e�ective drift velocity. The in uence of BW was already minimized by animproved cell design as described in [10].

8 Conclusions

The results shown in this paper con�rm that the actual design of drift tubesis adequate to achieve the expected performance in the range of magnetic�eld values which will be present in the CMS barrel muon detector. E�ciencyand resolution are, in all cases, good enough to meet the muon reconstructionand triggering requirements. Minor e�ects can also be foreseen in the bunchcrossing identi�cation capability. Some degradation is only to be expected inthe small region of the MB1 chambers close to � = 1:1 because of the veryhigh and non uniform radial magnetic �eld. It is a general conclusion of all thedescribed e�ects that the trigger processor will have to be carefully optimisedtaking into account chamber positioning in CMS. Studies of how to implementthis have been already done [11] and further work is under way.

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References

[1] CMS Technical Proposal, CERN/LHCC 94-38, LHCC/P1, 15 December 1994.

[2] F. Gasparini et al., Nucl. Instr. and Meth. A 336 (1993) 91.

[3] G. Barichello et al., Nucl. Instr. and Meth. A 360 (1995) 507.

[4] M. Benettoni et al., Performance of the Drift Tubes for the Barrel MuonChambers of the CMS Detector at LHC, Nucl. Instr. and Meth. A, in print.

[5] The CMS Muon Project. Technical Design Report, CERN/LHCC 97-32, 1997.

[6] Y.-H. Chang et al., Nucl. Instr. and Meth. A 311 (1992) 490.

[7] The CMS Magnet Project. Technical Design Report, CERN/LHCC 97-10, 1997.

[8] W. Blum, L. Rolandi, Particle Detection with Drift Chambers, Springer Verlag,Second Printing 1994.

[9] R. Veenhof, GARFIELD, a Drift Chamber Simulation Program User's Guide,Version 5.13, CERN Program Library W5050, 1995.

[10] A. Benvenuti et al., Simulations in the Development of the Barrel MuonChambers for the CMS experiment at CERN, Nucl. Instr. and Meth. A, in print.

[11] M. de Giorgi et al., Nucl. Instr. and Meth. A 398 (1997) 203.

11

Table Captions

Table 1: The drift velocity and corresponding maximum drift time and Lorentzangle for di�erent voltage and magnetic �eld settings.

12

Table 1

U [kV] BN [T] tmaxdrift[ns] �vdrift[�mns] �L[

�]

0 351�2 55,6�0,2

3.3/1.5/-1.5 0.5 356�2 54,7�0,2 10,4�2

1.0 394�1 49,5�0,2 26,4�2

0 346�2 56,4�0,2

3.6/1.8/-1.8 0.5 351�2 55,7�0,2 9,7�3

1.0 373�1 52,3�0,2 22,4�1

13

Figure Captions

Figure 1: Longitudinal view of a quadrant of the CMS detector showing theposition of the 4 barrel muon stations (MB1 to MB4) and also the forwardmuon system (ME1 to ME4). The interaction point is at the origin of thecoordinate system and the proton beams run along the z axis.

Figure 2: The magnetic �eld components parallel (Bz) and perpendicular (Br)to the proton beam axis inside the central muon chambers of the CMS de-tector. The shaded areas are the gaps between the detector rings shown in�g. 1.

Figure 3: Drift lines in a cell of the CMS barrel muon detector under thein uence of a magnetic �eld of 0.45 T parallel to the anode wires. The driftgas is Ar:CO2(85:15). The anode is a 50 micron diameter stainless steel wire.Top and bottom planes are made of 2 mm thick aluminium sheets insulatedfrom aluminium I beam cathodes by Lexan strips 0.5 mm thick. Two copperstrip electrodes 14 mm wide, mylar backed for insulation purposes, improve�eld uniformity.

Figure 4: Drift lines inside the cell in absence of magnetic �eld are shown ina). The presence of a magnetic �eld orthogonal to the chamber plane changesthe drift direction as shown in b) re ecting in a smaller apparent drift velocity.

Figure 5: Drift velocity as a function of the magnetic �eld B in the two con�g-urations: B parallel to the anode wires (BW ), and B perpendicular to the wiresand parallel to the electric �eld (BE). The chamber was placed orthogonal tothe beam.

Figure 6: Mean values of residuals to straight line �ts of tracks having hits inall 4 layers of a quadruplet, as a function of the distance to the wire, for datataken with BW = 0.8 T and BW = 0.18 T. The former value of BW will neverbe reached in the barrel chambers at CMS. The average values are taken for1 mm wide slices of distance.

Figure 7: Single wire resolution as a function of the magnetic �eld B in thetwo con�gurations: B parallel to the anode wires (BW ), and B perpendicularto the wires and parallel to the electric �eld (BE).

Figure 8: E�ciency as a function of the magnetic �eld B in the two con�gura-tions: B parallel to the anode wires (BW ), and B perpendicular to the wiresand parallel to the electric �eld (BE).

Figure 9: E�ciency as a function of the distance to the wire for di�erent valuesof BW .

14

Figure 10: Maximum drift time as a function of the magnetic �eld BW forseveral angles of incidence obtained by rotating the chamber around an axisparallel to the wires. Di�erent values are obtained for positive and negativemagnetic �elds indicating the asymmetrical behaviour of the drift tube.

Figure 11: The space-time relationship for BN = 0 T and BN = 1 T.

Figure 12: The average maximum drift time, calculated from (3), for a tripletof drift cells versus the drift distance in the intermediate cell. The vertical barsare the widths of a Gaussian �t, hence the mean time resolution. The dottedlines indicate an interval of �12:5 ns around the B=0 results correspondingto the proton bunch crossing frequency of 25 ns.

Figure 13: Single wire resolution for several values of the magnetic �eld com-ponent BN and of the angle of incidence �.

Figure 14: Average single wire e�ciency for several values of the magnetic�eld component BN and of the angle of incidence �.

Figure 15: The average maximum drift time, calculated from (3), for a tripletof drift cells versus the drift distance in the intermediate cell for BN = 0.9 Tand BW = 0.45 T. These magnetic �eld values will never be reached in CMS.The vertical bars are the widths of a Gaussian �t. The dotted lines indicatean interval of �12:5 ns corresponding to the proton bunch crossing frequencyof 25 ns.

15

1.26

8 m

3.95

4 m

6.61

m

5.68

m

6.66

m

7.24

m

8.49

5 m

9.75

m

10.6

3 m

10.8

3 m

6.45

m

10.8

6 m

10.9

1 m

14.5

3 m

14.5

6 m

14.9

6 m

4.905 m

1.811 m

ME

1

ME

3

ME

4

ME

2 M

E2

ME

3

ME

4

ME

1

ME

1

movement with field on: 0.5 cm, distributedC.M.S.Compact Muon Solenoid

Longitudinal View

Y

Z

g

η = 5.31

4.33

2 m

movement with field on: 1 cm

3.90

m

1.711 m1.9415 m

Field off

Field off

All dimensions are indicated with field off

0.00

m

η = 3.0

η = 2.4

η = 1.479

η = 1 η = 0.5η = 1.1

0.440 m

6.955 m

2.864 m2.700 m

3.800 m

7.380 m7.000 m

5.975 m

4.020 m

7.430 m

0.00 m

1.185 m1.290 m

0.00

0 m

2.93

5 m

2.950 m

MB1

MB2

MB3

MB4

MB1

MB2

MB3

MB4

MB1

MB2

MB3

MB4

Fig. 1.

16

z[m]

Br[T]

MB

1M

B2

MB

3M

B4

-0.4

-0.2 0

0.2

0.4

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46

z[m]

Bz[T]

MB

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46

Fig.

2.

17

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13 mm

40 mm

ElectrodeAnode wire

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��Cathode

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1.8 kV

Ground

Ground

-1.8 kV

3.6 kV

Fig. 3.

18

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13 mm

40 mm

ElectrodeAnode wire

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��Cathode

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Anode wire

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��Cathode

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b)

Drift

E

BB EDrift

a)

Drift

E

BB EDrift

Fig. 4.

19

B parallel to the wires (BW)B parallel to the electric field (BE)

Magnetic Field (T)

Drif

t Vel

ocity

(µm

/ns)

(3.3/1.5/1.5 kV)

50

51

52

53

54

55

56

57

58

59

60

0 0.2 0.4 0.6 0.8 1

Fig. 5.

20

(3.3/1.5/1.5 kV)

BW = 0.18 T

BW = 0.80 T

Distance to the wire (mm)

Dev

iatio

n fr

om li

near

ity (

mm

)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14 16 18

Fig. 6.

21

(3.3/1.5/1.5 kV)

B parallel to the wires (BW)

B parallel to the electric field (BE)

Magnetic Field (T)

Res

olut

ion

(mm

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

Fig. 7.

22

(3.3/1.5/1.5 kV)

Magnetic Field (T)

Effi

cien

cy (

%)

B parallel to the wires (BW)B parallel to the electric field (BE)

86

88

90

92

94

96

98

100

0 0.2 0.4 0.6 0.8 1

Fig. 8.

23

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16 18 20

BW = 0

BW = 0.4 T

BW = 0.6 T

BW = 0.8 T

Drift distance (mm)

Effi

cien

cy (

%)

Fig. 9.

24

B parallel to the wire (Bw)

φ = 0 o

φ = 14 o

φ = 24 o

B Field (T)

t max

(ns

)

320

330

340

350

360

370

380

390

400

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Fig. 10.

25

0 100 200 300 400Drift Time [ns]

02468

12141618

10

Dis

tanc

e fr

om A

node

[m

m]

B = 1.0 TN

B = 0 TN

Fig. 11.

26

0 2 4 6 8 10 12 14 16 18 20 Distance from Anode [mm]

340

360

380

400

420

440M

ean

Tim

e [n

s]

B = 1.0 TN

B = 0

Fig. 12.

27

100100

150

200

250

300

350

400

450

500

Degrees

Degrees

Degrees

00 0.2 0.4 0.6 0.8 1Magnetic Field Magnetic Field [T]

Sing

le W

ire

Res

olut

ion

[µm

]

Fig. 13.

28

98.0

98.2

98.4

98.6

98.8

99.0

99.2

99.4

99.6

99.8

100

Degrees

Degrees

Degrees

0 0.2 0.4 0.6 0.8 1

Magnetic Field [T]

Sing

le W

ire

Eff

icie

ncy

[%]

Fig. 14.

29

340

360

380

400

420

440

B = 0.9 TN

0 2 4 6 8 10 12 14 16 18 20 Distance from Anode [mm]

B = 0.45 TW M

ean

Tim

e [n

s]

Fig. 15.

30